Gaussians on Riemannian Manifolds for Robot Learning and Adaptive Control

This paper presents an overview of robot learning and adaptive control applications that can benefit from a joint use of Riemannian geometry and probabilistic representations. We first discuss the roles of Riemannian manifolds, geodesics and parallel transport in robotics. We then present several forms of manifolds that are already employed in robotics, by also listing manifolds that have been underexploited so far but that have potentials in future robot learning applications. A varied range of techniques employing Gaussian distributions on Riemannian manifolds are then introduced, including clustering, regression, information fusion, planning and control problems. Two examples of applications are presented, involving the control of a prosthetic hand from surface electromyography (sEMG) data, and the teleoperation of a bimanual underwater robot. Further perspectives are finally discussed with suggestions of promising research directions.

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